Respiratory Induced Resonance Offset (RIRO) handicaps the accuracy of the Proton Resonance Frequency Shift (PRFS) method of temperature mapping. We propose a compensation technique. Baseline images characterizing RIRO at a variety of respiratory cycle instants are acquired before a thermal treatment. During the treatment, the temperature evolution is found from two successive images and corrected for the additional contribution caused by RIRO using the pre-treatment baseline images acquired at the identical instances of the respiratory cycle. Our method is shown to improve the accuracy and stability of PRFS temperature maps in the presence of RIRO and motion in phantom experiments.